Nonintegrability, Separatrices Crossing and Homoclinic Orbits in the Problem of Rotational Motion of a Satellite

Abstract

It is well known that in hamiltonian systems the existence of transversal homoclinic orbit to a hyperbolic periodic solution leads to complicated behavior of phase trajectories and nonintegrability1,2. However, if we take an unstable equilibrium instead of a periodic solution, the situation is much more complicated. Devaney3 gave an example (the Neumann problem) of integrable system with transversal homoclinic orbit to the saddle equilibrium point.